Affiliations: Faculty of Mechanical Engineering, Belgrade University, Yugoslavia
Note: [1] This paper has been presented by the author on the 1st of June 1956 to the III Yugoslave Congress of applied Mechanics in Bled, and on the 5th of September 1956 to the IX International Congress of applied Mechanics in Brussels.
Note: [2] In this paper are given only the definition of the problem, the assumptions under which it has been considered, a summary of the solution of the problem, as well as the summary of the results obtained and that of the conclusions, without entering into details and mathematical deductions. There belong two appendices to this paper too, which on this occasion are omitted, but which represent together with the paper a complete work. In them has been discussed the mathematical treatment of the problem which is given in this paper (the deduction of the differential equations of the motion of a ship, determination of the constants which depend on the geometrical form of the ship and on the length of the waves, and so on). These appendices can be obtained on application to the author.
Abstract: The motion of a ship in a seaway was considered by A.N. Kriloff in his two well known papers [1] and [2] in 1896–98. In [1] A.N. Kriloff concluded that the difference between the hydrostatic distribution of buoyancy and the distribution following Gerstner’s theory of waves, the so-called Smith Effect, has no important influence on the motion of a ship, so that it can be neglected. This opinion has prevailed up the present. So, for instance, on the basis of that conclusion, G.P. Weinblum and M. St. Denis, have neglected the Smith Effect, when discussing in the paper [3] the motions of a ship in a seaway. In the present paper the author considers the motion of a ship in a seaway on the same assumption as A.N. Kriloff, except that he: a. takes into consideration approximately the influence of added mass; b. accepts the cosinusoidal wave profile, and c. substitutes the real hull surface by approximative analytical expressions corresponding to the coefficients and the main dimensions of a ship. For the case were the length of the waves λ is equal to the length of the ship L, the author shows that Smith Effect can not be neglected, and that the decreases of amplitudes caused by it can be over 50% for heaving, and over 30% for pitching. The author gives the diagrams by means of which it is possible to estimate approximatively Smith Effect, and to determine the heaving and the pitching of a ship in every particular case, when the waterplane coefficient α, the block coefficient δ and the main dimensions of a ship: the breadth B, the length L and the draft T are given.
